Category: mathematical biology

Dr. David M. Eddy is one of the rare people for whom the “Dr.” refers to both a medical and academic degree. Dr. Eddy received his Ph.D. in applied mathematics in 1978, ten years after becoming a medical doctor, and he’s been a pioneer in applications of mathematics to medicine ever since. His latest project sounds like a massive undertaking: a computer program called Archimedes, which is intended to represent the various aspects of human physiology well enough so that new drugs, tests, or procedures could be tried out on virtual human subjects before any actual humans went under treatment. A description of the project’s genesis and development appears in this story from Wired magazine.

The program was a kind of SimHealth: a vast compendium of medical knowledge drawn from epidemiological data, clinical trials, and physician interviews, which Eddy had laboriously translated into differential equations over the past decade. Those equations, Eddy hoped, would successfully reproduce the complex workings of human biology — down to the individual chambers of a simulated person’s virtual heart…. a soup-to-nuts model that would capture everything known by modern medicine, from the evolution of disease in different people — as shaped by factors like race, genetic risk, and number of hours spent doing yoga — to specific physiological details, such as the amount of heart muscle that dies in the hours after a heart attack and the degree to which medications like aspirin can limit that damage. Tests could be run in hours instead of years, and the model could be constantly updated with the latest research.

According to the article, the model could already do a very good job of predicting the results of previous clinical trials, and the next step—coming soon no doubt—was to have it ‘virtually’ conduct some drug trials, trials that might otherwise be too difficult, costly, or dangerous for drug companies to do themselves.

Every year Discover magazine lists its 100 Top Science Stories, and a number of these stories, particularly those involving physics and engineering, require a lot of math in their execution. Beyond that, however, four of the stories feature mathematics centrally. In numerical order:

In #51 A Computer Rosetta Stone we find a computer program that deciphers ancient heiroglyphics statistically. MIT computer scientist Regina Barzilay has developed the program, which compares unknown letters and words to letters and words of known languages in order to find parallels. When she tested it by seeing how much of ancient Ugaritic the program could decipher using the related language Hebrew as the ‘parallel’, the program correctly matched 29 of the 30 Ugaritic letters to their Hebrew equivalent, and 60% of the Ugaratic words that had Hebrew cognates. More importantly, it did the work in a matter of hours, whereas human translators needed decades (and the chance find of an ancient Ugaritic axe that had the word “axe” carved on it) to accomplish similar feats. While the program certainly cannot replace the intuition and feel for language that human scientists possess, “it is a powerful tool that can aid the human decipherment process,” and could already be of use in expanding the number of languages that machine translators can handle.

#60 Fighting Crime with Mathematics details the work of UCLA mathematicians Martin Short and Andrea Bertozzi who, along with UCLA anthropologist Jeff Brantingham, developed a mathematical model of the formation and behavior of crime ‘hotspots.’ After calibrating the model with real-world data, it appears that hotspots come in two varieties: “One type forms when an area experiences a large-scale crime increase, such as when a park is overrun by drug dealers. Another develops when a small number of criminals—say, a pair of burglars—go on a localized crime spree.” According to the work, the typical police reaction of targeting the hotspots appears to work much better on the first type of hotspot, but hotspots of the second type usually just relocate to a less-patrolled area. As the story notes, “By analyzing police reports as they come in, Short hopes to determine which type of hot spot is forming so police can handle it more effectively.”

There seems to be a steady stream of stories recently that remark on how some animals instinctively know the best way to do things. One example from this blog is Iain Couzin’s work on animal migration. And here’s another: #92 Sharks Use Math to Hunt. Levy flight is the name given a search pattern which has been long suspected by mathematicians of being one of the most effective hunting strategies when food is scarce. David Sims of the Marine Biological Association of the United Kingdom logged the movements of 55 marine animals from 14 different species over 5,700 days, and confirmed that the fish movements closely matched Levy flight. (The marine animals included tuna and marlin, by the way, but sharks always get the headlines.)

#95 Rubik’s Cube Decoded covers a story already mentioned on this blog about “God’s Number”, the maximum number of moves that an omniscient being would need in order to solve any starting position of Rubik’s cube. The answer, as you can read in this story or by reading my earlier blog post, is 20.

The whole Top 100 is worth going through as well. It’s remarkable to realize how much and how quickly science is learning in this day and age.

Each year the magazine Popular Science dubs 10 young scientists their “Brilliant 10″, highlighting the scientists’ work and its implications. In the 2010 edition, more than a few of the profiled rely on mathematics. The work of two, Iain Couzin and Paul Rabadan, are especially mathematical and I’ll mention them here.

This is, of course, one of the great strengths of mathematics: once abstracted, it is easy to recognize a pattern that occurs in different places. Some of Couzin’s earlier work—featured in articles in National Geographic and the NY Times, for instance—involved divining the rules that army ant colonies use to direct their devastating raids. His most recent work, mentioned in Discover, provides an explanation for the large migrations seen in so many animal species. The model, if correct, also provides a warning: tampering with the migrating herds, through hunting or habitat alteration, could devastate the migration instinct itself.

Migration could disappear in a few generations, and take many more to come back, if at all. Indeed, bison in North America no longer seem able to migrate, a fate that may soon be shared by wildebeest in the Serengeti. Migration may vanish at a scale measured in human years, and recover at time scales measured in planetary cycles.

Raul Rabadan, “the Outbreak Sleuth” has a background in string theory, but his numerical experience is serving him well now in his hunt for the agents behind various biological diseases.

Raul Rabadan hunts deadly viruses, but he has no need for biohazard suits. His work does not bring him to far-flung jungles. He’s neither medical doctor nor epidemiologist. He’s a theoretical physicist with expertise in string theory and black holes, and he cracks microbial mysteries in much the same way he once tried to decode the secrets of the universe: He follows the numbers.

Rabadan has been a pioneer of a data analysis technique called Frequency Analysis of Sequence Data that has been able to pinpoint previously unknown viruses as the cause of major disease outbreaks in various animal (and human) populations. Some of his work focused on tracing the origins of the H1N1 swine flu virus, with articles about the work appearing in Wired and online at CNN and USA Today.

This NY Times article details the efforts of Dr. Giulio Tononi to develop a means to measure a person’s level of consciousness as easily as a blood pressure sleeve measures a person’s blood pressure. Dr. Tononi is one of the world’s experts on consciousness, especially that peculiar form of half-consciousness known as sleep. While most people, researchers included, have long thought of consciousness as a kind of synchronization of brain waves, Dr. Tononi noticed that in particular kinds of unconsciousness, like during epileptic seizures, brain waves were even more synchronized than during wakeful periods. It seemed a new paradigm for consciousness was required. And for that paradigm, Dr. Tononi turned to information theory.

While in medical school, Dr. Tononi began to think of consciousness in a different way, as a particularly rich form of information. He took his inspiration from the American engineer Claude Shannon, who built a scientific theory of information in the mid-1900s. Mr. Shannon measured information in a signal by how much uncertainty it reduced. There is very little information in a photodiode that switches on when it detects light, because it reduces only a little uncertainty…. Our neurons are basically fancy photodiodes, producing electric bursts in response to incoming signals. But the conscious experiences they produce contain far more information than in a single diode. In other words, they reduce much more uncertainty.

Tononi has developed a measure called phi that seems to track how rich in information a mental state is, and the article mentions some preliminary medical work that is lending support to his model. The research is in its infancy and much more work is needed, but the same could be said for all science-based inquiries into consciousness. The point here is that the Dr. Tononi’s work “translating the poetry of our conscious experiences into the precise language of mathematics” holds promise—at the very least, enough promise to warrant featuring in this article.

Malaria affects hundreds of millions of people throughout the world annually, killing over one million of them. Almost all of these victims live in third-world countries, and many of them are children—one estimate is that a child dies of malaria every 30 seconds. This Newsweek article, by Daniel Lyons, describes Intellectual Ventures, an American start-up that is trying to use first-world know-how to combat the disease. The company got its start when its founder, Nathan Myhrvold, was told by Bill Gates, “Come up with some good ideas and I’ll come up with some money to pursue them.” Some of the inventors mentioned are mathematicians, and one of those ideas is a massive mathematical model of the disease that “lets researchers see the effect of potential vaccines that don’t exist, so they can choose which one to develop.” Other ideas are also mentioned and many of them, as Myhrvold admits, sound farfetched. But really, as Lyons concludes, how can you argue against trying?

Addendum: In another development on the malaria front, researchers at Case Western Reserve University recently developed techniques that can quickly identify drug resistance in strains of malaria. The new technique is expected to “enable the medical community to react quickly to inevitable resistance and thereby save lives while increasing the lifespan of drugs used against the disease,” according to the article “New Methods, New Math Speed Detection of Drug-Resistant Malaria” from ScienceDaily. The key—developed by mathematics Prof. Peter Thomas and a student, Drew Kouri—involved “using a nontraditional mathematical analysis that’s proved more accurate than traditional methods.” (That ‘nontraditional analysis’ mentioned, by the way, was simply switching to polar coordinates.)

This brief article from US News & World Report describes a new mathematical model of ischemic wounds. Ischemic wounds are wounds that do not get as much blood flow as normal wounds, and they affect six and a half million Americans each year. The model, developed by Avner Friedman of Ohio State, includes factors that mimic the actions of healing agents like white blood cells, capillary sprouts, blood-vessel-forming proteins and oxygen concentrations, and is the first to accurately predict healing times for these kind of wounds. The hope is that models like this are “the start of something that could give valuable insight to the wound healing problem in the future.”

This article (Spanish-language) in La Nacion describes work whose roots lie in an old project of Sigmund Freud and Carl Jung, among others. Both of those luminaries spent considerable time and effort on the ‘word association problem': trying to divine when and why certain words were associated with each other in many people’s minds. Mariano Sigman, Martin Elias and Flavia Bonomo of the University of Buenos Aires applied mathematics to the problem, using a huge corpus of text from newspapers and books to develop a metric which determines how “close” and “far” different words typically are from each other. The associations given by their metric appear to do a pretty good job mirroring the responses people give when given a word and asked to say what pops into their head.

This story by Clive Thompson from the NY Times Magazine examines networks and the signals that travel over them–only the network and the signals aren’t made of wires and electric impulses, the network is the social network of friends and relations and the signals are behaviors. A number of scientists have been using the mathematics of networks to analyze the impact that the behaviors of peoples’ friends and relations have on their own behaviors, and how certain behaviors sometimes get “transmited” through the network in ways startlingly like more physical networks. This article (free registration required) describes some of those scientists and their findings.

Wired magazine presents the best science visualization videos of 2009:

The Department of Energy honored 10 of this year’s best scientific visualizations with its annual SciDAC Vis Night awards, at the Scientific Discovery through Advanced Computing conference (SciDAC) in June. Researchers submitted visualizations to the contest, and program participants voted on the best of the best. From earthquakes to jet flames, this gallery of videos and images show how beautiful (and descriptive) visual data can be.

All of these videos are of course essentially illustrations of mathematical models, models that are so complex that just making the individual frames of the videos requires heavy-duty mathematics and heavy-duty computational power.

This TIME magazine article describes a literal marriage between math and medicine: the couple made up of transplant surgeon Dory Segev and his mathematician wife Sommer Gentry. Together, Segev and Gentry developed a new way to more efficiently match kidney donors with the more than 60,000 Americans awaiting transplants. Gentry was also interviewed by various radio, TV, and newspaper outlets.